Method for a satellite station keeping

Abstract: A method and apparatus for satellite station keeping is disclosed in which four thrusters (20-26) are mounted on the anti-nadir face of the satellite with their direction of thrust passing through the center of mass of the satellite. The thrust lines of the north pair of thrusters (20-22) and the south pair of thrusters (24-26) make an angle ϑ with the satellite north-south axis in a northern and southern direction respectively. The thrusters are laterally separated and slewed by an angle α about the north-south axis. Each thruster produces three components of ΔV, i.e. normal, tangential and radial (toward the Earth), thereby providing complete control of the three orbit vectors, inclination, eccentricity and mean motion. In the event of failure of a thruster, the thruster diagonally opposite the failed thruster is shutdown and the remaining diagonal pair of thruster is used to maintain station keeping.

Description: The invention relates to a method of station keeping for a three-axis stabilized satellite moving along an orbit about the earth having an ascending node and a descending node, the satellite comprising a north and a south pair of thrusters mounted in a generally rectangular configuration on an anti-nadir face of the satellite, the lines of thrust of each thruster being directed through the center of mass of the satellite and the pairs of thrusters being configured to comprise a northwest thruster, a northeast thruster, a southwest thruster and a southeast thruster , wherein: the north pair and the south pair of thrusters are canted away from the anti-nadir face in a north and a south direction, respectively by a first predetermined angle  from a north-south axis passing through the center of mass of the satellite; the northeast and southeast thrusters are slewed in an east direction about the north-south axis by a second predetermined angle α and the northwest and southwest thrusters are slewed in a west direction about the north-south axis by the second predetermined angle α; the south pair of thrusters is fired in a first position near the descending node to produce a first predetermined satellite velocity component ΔV N in a normal direction; the north pair of thrusters is fired in a second position near the ascending node to produce a second predetermined satellite velocity component ΔV N in a normal direction. A method of the afore-mentioned kind is disclosed in document "ELECTRONICS AND COMMUNICATIONS ENGINEERING JOURNAL", Vol. 4, No. 3, June 1992, London (GB), pages 153-162: FEARN, D.G. "ION PROPULSION - A TECHNOLOGY FOR IMPROVING THE COST-EFFECTIVENESS OF LARGE COMMUNICATION SATELLITES". Synchronous satellites orbit the earth with the same revolution rate as that of the earth. Accordingly, the satellite appears above a fixed point on the earth. Hence, synchronous satellites are often referred to as geostationary satellites and operate within a stationary orbit. Synchronous satellites are useful for many applications including weather and communication applications. It is generally well-known in the art that various forces act on synchronous satellites to move the satellite out of stationary orbit. These forces are due to several sources including the gravitational effects of the sun and moon, the elliptical shape of the earth and solar radiation pressure. To counter these forces, synchronous satellites are equipped with propulsion systems that are fired at intervals in order to maintain station in a desired orbit. This requires control of the inclination, eccentricity and mean motion of the satellite. Inclination is the north-south position of the satellite relative to the earth's equator. Eccentricity is the measure of the non-circularity of the satellite orbit. That is, the measure of the variation of the distance the satellite is from the earth as the earth and the satellite rotate. Finally, mean motion is the average position of the satellite in an east-west direction relative to a sub-satellite point on the earth. For a more detailed discussion see "Controlling a stationary orbit using electric propulsion" by Bernard M. Anzel, presented to the 1988 International Electric Propulsion Conference in West Germany. Station keeping was first achieved with a spin-stabilized communication satellite launched in 1964. Current satellites are either spin-stabilized or three-axis stabilized satellites. Spin-stabilized satellites use the gyroscopic effect of the satellite spinning to help maintain the satellite orbit. For certain applications, the size of the satellite militates in favour of a three-axis stabilization scheme. Current three-axis stabilized satellites use separate sets of thrusters to control north-south and east-west motions. The north thrusters produce the required north-south change in satellite velocity, or ΔV, to control orbit inclination. The east thrusters and west thrusters produce the required combined east-west ΔV to control orbit mean motion and eccentricity. For each of these three maneuvers, thrusters are fired in pairs to cancel torques since the thrust directions do not pass through the satellite center of mass. Furthermore, there are three separate maneuvers performed at different times as required by the physics of the perturbations. The frequency of these maneuvers are typically every fourteen days for both the north-south maneuver and the pair of east-west maneuvers (east and west firings occur approximately ½ orbit apart or about 12 hours) when using five pound thrusters with liquid propulsion. Document US-A-5 020 746 discloses a three-axis-stabilized satellite for which station keeping is provided using only two thrusters mounted on the anti-nadir face of the satellite. A north thruster is canted away from the face at an angle  from the north-south axis of the satellite in a northern direction and a south-thruster is canted away from the face at an angle  from the north-south axis in a southern direction. Both thrusters are also translated to the east or west along an east-west axis of the satellite and swivelled at variable angles α 1 and α 2 , respectively. The document discloses a technique for determining the angles α 1 and α 2 and the firing positions of the thrusters in order to maintain the satellite in a stationary orbit. A two-thruster system such as disclosed in the aforementioned document is constrained in several respects. In order to control west motion as well as north-south motion, the truster mounting locations must be customized for the particular satellite station location. Notwithstanding this customization only a partial control of eccentricity is achieved. Also, in order to counter the eccentricity built-up resulting from a failure of one of the two thrusters, a back-up thruster must be provided. Document "ELECTRONICS AND COMMUNICATIONS ENGINEERING JOURNAL", Vol. 4, No. 3, June 1992, pp. 153-162, mentioned at the outset, discloses ion propulsion systems to be used as thrusters for a three-axis stabilized spacecraft. In Fig. 10 of this document various mounting configurations for ion thrusters on the spacecraft are illustrated. The orientation of the ion thrusters is primarily determined by the requirement to avoid direct ion beam impingement on the solar arrays of the space-craft. One of the illustrated thruster mounting configurations (Fig. 10d) provides for four thrusters on the anti-nadir face of the spacecraft, more specifically with two thrusters each on the edge between the anti-nadir face and the upper and lower surface, respectively, of the spacecraft. The lines of thrust of these four thrusters are directed through the center of gravity of the spacecraft. It is suggested to fire the thrusters in pairs, namely the northern pair around one node of the orbit and the southern pair around the other node. The document discusses the effect generated if one thruster of a pair is used by itself. Depending on the particular configuration used the document insofar makes reference to unacceptable east-west drift and to out-of-balance forces having effect on the orbital parameters. It is, therefore, an object underlying the invention to provide a method for satellite station keeping in which thruster mounting location is independent of satellite station location and which does not require a back-up thruster. In particular, the invention shall provide a method for maintaining the satellite in a stationary orbit through the simultaneous control of tangential, radial and normal acceleration components of thrust. In accordance with the present invention, this object is achieved through a method as specified at the outset and being characterized in that each of the four thrusters is associated to one individual firing time duration each and that the four time durations are set such as to simultaneously produce predetermined normal ΔV N , tangential ΔV T and radial ΔV R satellite velocity components ΔV to maintain the desired satellite orbit with respect to inclination, mean motion and eccentricity. Accordingly, the invention teaches to use four thrusters which are mounted on the anti-nadir face of the three-axis stabilized satellite with their directions of thrust passing through the center of mass of the satellite. The thrust lines of the north pair of thrusters and the south pair of thrusters make an angle , of for example 36°, with the satellite north-south axis in a northern and southern direction, respectively. The thrusters are laterally separated and slewed by an angle α, of for example 10°, about the north-south axis. The four thrusters provide complete control of the three orbit vectors, namely inclination, eccentricity and mean motion. Each thruster produces three components of ΔV, i.e. normal, tangential and radial (toward the earth), since their lines of thrust are directed through the satellite center of mass. With the configuration provided by the present invention, each of the north pair of thrusters is fired near the orbit ascending node and each of the south pair of thrusters is fired near the orbit descending node. Each thruster firing produces tangential and radial ΔV components, which control east-west motion, simultaneously with the normal ΔV component which controls north-south motion. In the event of failure of a thruster, the corresponding diagonally located thruster may be shut down and a third, simultaneous firing of the two remaining thrusters is performed midway between the ascending and descending nodes. This third firing produces equal ΔV components, resulting in normal and tangential ΔV cancellations but additive radial components. The radial components produced by this third firing cancel the eccentricity error created by the firing at the ascending and descending node. The invention will be better understood in connection with the drawings in which: Fig. 1 shows a three-axis stabilized satellite in a stationary orbit about the earth in two different positions to illustrate the improved method of satellite station keeping of the present invention; Fig. 2 shows a simplified 3-dimensional view of a three-axis satellite employing the four thruster system of the present invention; and Fig. 3a and 3b depict the burn arcs using each of this diagonal pairs of the thrusters to achieve satellite station keeping in the event of a failure of one of the thrusters in the four thruster system of the present invention. Referring now to the drawings and initially to Figure 1, a three-axis stabilized satellite 10 is shown in a stationary orbit about the Earth. A set of local coordinates for the satellite 10 is defined by the local vertical 12, by an east-west axis 14 and a north-south axis 16. The origin of the coordinates is the center of mass (C.M.) of the satellite 10. The local vertical 12, as shown in Figure 1, is the line through the Earth and satellite 10 which represents the nadir and anti-nadir directions. The nadir direction is the direction toward the Earth, and the anti-nadir direction is the direction away from the Earth. Figure 1 shows the satellite 10 in a first position A and a second position B to illustrate the location where the thruster firings take place. The cross-hatching in Figure 1 is intending to indicate the burn arc of the thrusters. Referring now to Figure 2, four thrusters 20, 22, 24, and 26 are mounted on the anti-nadir face 28 of the satellite 10. The four thrusters are canted away from the anti-nadir face by an angle  so that the thrust lines pass through the satellite center of mass. The north thruster pair 20, 22 are preferably mounted as close to the north end of the face 28 as is structurally possible. Likewise, the south thruster pair 24, 26 are mounted as close to the south end of the face 28 as is structurally possible. This mounting will minimize the cant angles of each pair and therefore minimize the cosine loss. The cosine loss is a geometric inefficiency in that for each unit of ΔV which a thruster produces, a smaller amount (equal to the cosine of the cant angle) appears in the north-south direction. The thrust lines of the north thrusters 20 and 22 and the south thrusters 24 and 26 make the angle , of for example 36°, with the north-south axis 16 in a northern and southern direction respectively. In addition to the cant angle  away from the anti-nadir face, the thrusters are also laterally separated and slewed by an angle α about the north-south axis 16. The slew angle must be large enough to effectively control the orbit eccentricity. The slew angles are determined from the tangential ΔV requirements imposed by the maximum solar force to satellite mass ratio to be encountered during on-station life. This then determines the horizontal separation for both the north and south thruster pairs along the anti-nadir face. A slew angle of approximately 10-12° is appropriate. Due to small changes in the center of mass of the satellite over time, both the slew angle α and the cant angle  may need to be changed. This angle modification may be accomplished by a conventional gimble and servo mechanism, not shown. The four thrusters 20-26 provide complete control of the three orbit vectors, namely, inclination, eccentricity and mean motion. Each thruster produces three components of ΔV, i.e. normal, tangential and radial (toward the Earth), since their lines of thrust are directed through the satellite center of mass. In most cases, the optimum time for providing north-south corrections to maintain the required inclination is at a right ascension (R.A.) of 90° for negative acceleration (south correction) and 270° for positive acceleration (north correction). (Right ascension is the angle measured in the equatorial plane from a reference position of the sun at vernal equinox to the satellite position). This is because most changes in inclination are produced by forces acting along an R.A. of 90°. In accordance with the present invention, the north thrusters 20 and 22 provide negative acceleration and are fired at R.A. = 90° while the south thrusters 24 and 26 provide positive acceleration and are fired at R.A. = 270° . If as shown in Figure 1 the firing arcs are equal, each pair of thrusters will provide one-half the required north-south velocity increment. Those skilled in the art will recognize that the frequency with which the thrusters are fired may vary without departing from the scope of the present invention. While both north thrusters 20, 22 are fired near the orbit ascending node (R.A. = 90°), and both south thrusters 24, 26 are fired near the orbit descending node (R.A.= 270°), such firings need not occur simultaneously. For example, the northwest thruster 20 may be fired before the ascending node and the northeast thruster 22 fired after the ascending node and a similar sequence would be followed for the south pair of thrusters at the descending node. In any event, these firings produce additive changes in inclination in a direction opposite to the effect of the sun/moon gravity perturbation. If the ΔV's produced by the firing of the north pair and south pair of thruster are equal, the radial components are equal, resulting in no net change in the orbit eccentricity. However, the radial ΔV components (always toward the Earth's center) produce generally unwanted additive eastward shifts in the mean longitude. The north thrusters 20 and 22 produce positive and negative tangential components of ΔV respectively. A net tangential ΔV which can be either positive or negative is, therefore, available. This positive or negative net tangential ΔV is likewise available when firing the south thrusters 24 and 26. This versatility permits complete control of the vector eccentricity component along a coordinate axis defined by the line connecting the centroids of the north and south thrusting arcs. The tangential ΔV also provides simultaneously, the correction in mean motion necessary to counter the triaxiality perturbation, as well as the aforementioned eastward motion of the mean longitude arising from the radial ΔV components. The inclination vector is completely controlled by the sum of the north-south ΔV components produced by the firings of the north and south pairs of thrusters. However, the firings need not be equal; in fact, by making them deliberately unequal, the difference in their radial components can be used to control the vector eccentricity component along a coordinate axis orthogonal to that connecting the north and south thrusting arc centroids. Thus, the ΔV components required for each of the four thrusters will, in general, be unequal and vary with the perturbations; the thruster ΔV components controlling four orbit parameters, inclination, mean motion and two orthogonal eccentricity components. The two orthogonal eccentricity components produce the necessary vector eccentricity change to counter the effects of the solar radiation perturbations. The ΔV components developed by the four thruster 20(N A+ ),22(N A- ),24(S D+ ), and 26(S D- ) are shown in the Chart below. ΔV COMPONENTS Thruster ΔV N (Normal) ΔV T (Tangential) ΔV R (Radial) N A+ South East Nadir N A- South West Nadir S D+ North East Nadir S D- North West Nadir ΔV R and ΔV T are related to ΔV N through the cant and slew angles  and α, respectively. ΔV R = ΔV N tan  ΔV T = ΔV N tan  tan α . The four values of ΔV N are: Δ V N ( N A + ) = 1/2 {[1/2(Δ V DT +Δ V ET )/tan tanα ] + [1/2(Δ V IN -Δ V ER /tan)]} Δ V N ( N A - ) = 1/2 {[-1/2(Δ V DT +Δ V ET )/tan tanα ] + [1/2(Δ V IN -Δ V ER /tan)]} Δ V N ( S D + ) = 1/2 {[1/2(Δ V DT -Δ V ET )/tan tanα ] + [1/2(Δ V IN +Δ V ER /tan)]} Δ V N ( S D - ) = 1/2 {[-1/2(Δ V DT -Δ V ET )/tan tanα ] + [1/2(Δ V IN +Δ V ER /tan)]} where: ΔV DT = Required total tangential ΔV to control longitude mean motion. ΔV ET = Required total tangential ΔV to control orbit eccentricity component along axis connecting firing points. ΔV ER = Required total radial ΔV to control orbit eccentricity component along axis perpendicular to axis connecting firing points. ΔV IN = Required total normal ΔV to control orbit inclination. The thruster firing time duration T P is given by: T P ≐ 2 ω e sin -1 ω e 2 m ·Δ V N F cos ω e = earth rate, M = spacecraft mass, F = engine thrust and ΔV N has four values corresponding to each of the four thruster (N A+ , N A- , S D+ , S D- ) as specified by the equations above. The burn time per thruster (for a 17.7 millinewton thrust level) will average about one hour per day for normal operation. Complete orbit control can still be maintained in the event of a failure of a pair of thrusters, provided that the failed thruster pair is diagonal, e.g., either 20 and 26 or 22 and 24. The nodal firings, occurring at positions A and B, for the remaining pair provide complete control of inclination and mean motion; however, the eccentricity will be incorrect. A third firing is performed at R.A. = 0° or R.A. = 180°, depending on which diagonal pair are available. At the third firing both thrusters are fired with equal ΔV components, resulting in normal and tangential ΔV cancellations. The radial components, however, will be additive and will provide the necessary eccentricity control. The time of firing and burn duration is chosen to nullify both the incorrect eccentricity produced by the nodal firings in addition to that produced by solar force. Thus, upon failure of any one of the thrusters 20-26, the corresponding diagonal thruster would be shut down and the firing procedure outlined above would be followed. There are two cases, either a) thruster 20(N A+ ) and thruster 26(S D- ) are used, or b) thruster 22(N A- ) and thruster 24(S D+ )are used. The location along the orbit of the burn arcs are illustrated in Figures 3a and 3b. There are three burn arcs per orbit. Since the burn arcs at the nodal crossings (R.A. = 90° and R.A. = 270°) are performed by single thrusters in the failure case, they will each require about twice the burn time as for the nominal case, i.e. about 2 hours per thruster per day on the average. The third burn is performed by both thrusters equally and the required burn time per thruster per day is about 2/3 hour on the average for a slew angle of 10°. The burn arcs depicted in Figures 3a and 3b are shown for sun positions at the equinoxes. The length of the third burn will not be equal for either equinox, and will have slightly altered centroid locations along the orbit for other times of the year.

Claims: A method of station keeping for a three-axis stabilized satellite (10) moving along an orbit about the earth having an ascending node and a descending node, the satellite comprising a north (20/22) and a south (24/26) pair of thrusters mounted in a generally rectangular configuration on an anti-nadir face (28) of the satellite (10), the lines of thrust of each thruster (20 - 26) being directed through the center of mass (C.M.) of the satellite (10) and the pairs (20/22, 24/26) of thrusters being configured to comprise a northwest thruster (20), a northeast thruster (22), a southwest thruster (24) and a southeast thruster (26), wherein: the north pair (20/22) and the south pair (24/26) of thrusters are canted away from the anti-nadir face (28) in a north and a south direction, respectively by a first predetermined angle () from a northsouth axis (16) passing through the center of mass (C.M.) of the satellite (10); the northeast (22) and southeast (26) thrusters are slewed in an east direction about the north-south axis (16) by a second predetermined angle (α) and the northwest (20) and southwest (24) thrusters are slewed in a west direction about the north-south axis (16) by the second predetermined angle (α); the south pair (24/26) of thrusters is fired in a first position (A) near the descending node to produce a first predetermined satellite velocity component (ΔV N ) in a normal direction; the north pair (20/22) of thrusters is fired in a second position (B) near the ascending node to produce a second predetermined satellite velocity component (ΔV N ) in a normal direction, characterized in that each of the four thrusters (20, 22, 24, 26) is associated to one individual firing time duration each and that the four time durations are set such as to simultaneously produce predetermined normal (ΔV N ), tangential (ΔV T ) and radial (ΔV R ) satellite velocity components (ΔV) to maintain the desired satellite orbit with respect to inclination, mean motion and eccentricity. The method of claim 1, characterized in that each of the four firing time durations of the four thrusters (20/N A+ , 22/N A- , 24/S D+ , 26/S D- )is based upon a corresponding one of four change in velocity quantities (ΔV N (N A+ ), ΔV N (N A- ), ΔV N (S D+ ), ΔV N (S D- )) given by the following equations: a) ΔV N (N A+ ) = 1/2{[1/2(ΔV DT +ΔV ET )/tan tanα] + [1/2(ΔV IN -ΔV ER /tan)]} b) ΔV N (N A- ) = 1/2{[-1/2(ΔV DT +ΔV ET )/tan tanα] + [1/2(ΔV IN -ΔV ER /tan)]} c) ΔV N (S D+ ) = 1/2{[1/2(ΔV DT -ΔV ET )/tan tanα] + [1/2(ΔV IN +ΔV ER /tan)]} d) ΔV N (S D- ) = 1/2{[-1/2(ΔV DT -ΔV ET )/tan tanα] + [1/2(ΔV IN +ΔV ER /tan)]}, where ΔV DT is the required total tangential satellite velocity component ΔV T to control longitudinal mean motion, ΔV ET is the required total tangential satellite velocity component ΔV T to control orbit eccentricity along an axis interconnecting the firing positions (A, B), ΔV ER is the required total radial satellite velocity component ΔV R to control orbit eccentricity along an axis perpendicular to the axis interconnecting the firing positions (A, B), and ΔV IN is the required total normal satellite velocity component ΔV N to control orbit inclination. The method of claim 1 or 2, characterized in that the combined firings of the thrusters (20, 22, 24, 26) produces a total tangential satellite velocity component (ΔV T ) to also control orbit eccentricity along a first axis interconnecting the ascending and descending nodes, and a total radial satellite velocity component (ΔV R ) to control orbit eccentricity along a second axis perpendicular to the first axis. The method of any of claims 1 - 3, characterized in that the northwest thruster (20) is fired before the orbit ascending node and the northeast thruster (22) is fired after the orbit ascending node. The method of any of claims 1 - 4, characterized in that the southwest thruster (24) is fired before the orbit descending node and the southeast thruster (26) is fired after the orbit descending node. The method of any of claims 1 - 5, characterized in that the first predetermined angle () is 36°. The method of any of claims 1 - 6, characterized in that the second predetermined angle (α) is approximately 10 - 12°. The method of claims 6 or 7, characterized in that the first () and the second (α) predetermined angle are adapted to be modified by means of a gimble servo mechanism. The method of any of claims 1 - 8, characterized by the following steps: shutting down a diagonal one of the four thrusters (20, 22, 24, 26) in response to failure of its corresponding diagonal thruster; firing the north thruster near the orbit ascending node; firing the south thruster near the orbit descending node; and simultaneously firing the north and south thrusters midway between the ascending and the descending node. The method of claim 9, characterized in that the ascending node has a right ascension angle (RA) of 90°, that the descending node has a right ascension angle (RA) of 270°, that the north thruster (22) is the eastern one of the north pair of thrusters (20/22), that the south thruster (24) is the western one of the south pair of thrusters (24/26) and that the simultaneous firing occurs at a right ascension angle (RA) of 0°. The method of claim 9, characterized in that the ascending node has a right ascension angle (RA) of 90°, that the descending node has a right ascension angle (RA) of 270°, that the north thruster (20) is the western one of the north pair of thrusters (20/22), that the south thruster (26) is the eastern one of the south pair of thrusters (24/26) and that simultaneous firing occurs at a right ascension angle (RA) of 180°.

Inventors: ANZEL BERNHARD M, ANZEL, BERNHARD M.
Applicants: HUGHES AIRCRAFT CO, HUGHES AIRCRAFT COMPANY
Application year: 1994
Main classification: B64G1
IPC codes: B64G1